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Forthcoming events in this series
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Sound Propagation in an Urban Environment (J R Ockendon, D Allwright and Chris E Breward)
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Separation of Variables for PDEs. A new look at an old subject.
Abstract
Taking a view common in the finite element analysis, we interpret
the first N terms of the usual Fourier series solution as the exact
solution of an approximating problem in a subspace spanned by the
eigenfunctions of the underlying Sturm Liouville problem. This view
leads to a consistent solution technique for the heat, wave and
Poisson's equation, and allows an analysis of the error caused by
truncating the Fourier series. Applications to a variety of problems
will be discussed to demonstrate that the analytic approach remains a
valuable complement to purely numerical methods.
The talk is intended for students with an interest in actually
solving partial differential equations. It assumes a standard
background in undergraduate mathematics but not necessarily prior
exposure to the subject. The goal is to show that there is more to
separation of variables than is apparent from standard texts on
engineering mathematics.
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